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Abstract

A program is disclosed that calculates correlation coefficient value without disclosing each data owned by different person.

Country

United States

Language

English (United States)

This text was extracted from an ASCII text file.

This is the abbreviated version, containing approximately
55% of the total text.

A Method for Calculating Correlation Coefficient without
Disclosing
Each Data

A program is
disclosed that calculates correlation
coefficient value without disclosing each data owned by different
person.

Two person A and
B own data ai and bi (1 le i le n) and
they do not want to disclose the data each other but they want to
calculate the correlation coefficient value of the ai and bi. This
program calculates the correlation coefficient value r without
disclosing the each data. r is defined
as following formula.
r = < sum from i=1 to n of (a(i) -
aav)(b(i) - bav) > over
< sig(a) sig(b) >
aav and bav are average of a(i) and
b(i). Siga and sigb are
standard deviation of a(i) and
b(i). In this disclosure,
r is defined as following for convenience
by normalizing the
average and the standard deviation.
r = sum from i=1 to n of ai bi

This is inner
product of n dimension vector va and vb.

A and B use this
program each other. At first, this
program of A and B decide and share a set of base vectors of
orthonormal system { vei } (1 le i le n) by using random number. In
this orthonormal system, each component is transferred as follows.
< aip = ( va , vei ) > habove
< bip = ( vb , vei ) >
r can be expressed by using aip and bip
as follows, because
the inner product is not changed by
orthogonal transformation.
r = sum from i=1 to n of ai bi = sum
from i=1 to n aip bip